Question

An investor obtained a fully amortizing mortgage five years ago for $95,000 at 11-percent for 30 years. Mortgage rates have dropped, so that a fully amortizing 25-year loan can be obtained at 10-percent. There is no prepayment penalty on the mortgage balance of the original loan, but three points will be charged on the new loan and other closing costs will be $2,000. All payments are monthly.

Required:
a. Should the borrower refinance if he plans to own the property for the remaining loan term? Assume that the investor borrows only an amount equal to the outstanding balance of the loan.
b. Would your answer to part (a) change if he planned to own the property for only five more years?

Answer 1

a) yes, you should refinance the loan

b) yes, you should refinance the loan

Step-by-step explanation:

the original monthly payment = $904.71

after 60 payments, the principal owed = $838.79

the difference between both payments = $904.71 - $838.79 = $65.92

in order to determine whether the loan should be refinanced or not, we must find the present value of refinancing costs:

are 300 payments of $65.92 worth more than $2,000?

PV = $65.92 x 110.162 (PVIFA, 0.833%, 300 periods) = $7,261.88 ≥ $2,000

PV = $65.92 x 47.07(PVIFA, 0.833%, 60 periods) = $3,102.85 ≥ $2,000